Consensus and Products of Substochastic Matrices: Convergence Rate With Communication Delays
研究了领导者-跟随者多智能体系统在通信延迟下达成一致的收敛速度，通过次随机矩阵乘积构建度量标准，给出了收敛速度与网络结构、权重上限和延迟大小的关系，以及特殊拓扑下的有限收敛时间上界。
This study analyzes the convergence rate of leader–follower multiagent consensus under communication delays by developing a measure standard utilizing products of substochastic matrices. Through the construction of augmented auxiliary digraphs, which combine the binary relations composition, a comprehensive analysis of the leader–follower consensus dynamics is conducted. A mathematical representation of the least convergence rate of the system is established, which is closely related to the network structure, the upper bound of weight factors as well as the size of time delays. Moreover, an upper bound on the finite convergence time of the system with special topological structures, such as chain graph, star graph, and tree graph is given. At last, simulated examples are presented to confirm the theoretical findings.